Not that it will get you anywhere but this birth is probably Edward's daughter
Betsy Holdgate Q2 1856 Pickering 3[5]6 9?
Anne Holdgate Q1 1838 Pickering 24/355
George Holdgate Q3 1847 Pickering 24/473
William Holldgate (sic) Q4 1849 Pickering 24/486
Mary Jane Holdgate Q2 1851 Pickering 24/580
Death of William Holldgate (sic) Q4 1849 Pickering 24/343
Poor chap, the spelling of Holldgate in BOTH birth and death entries makes me think that they were both done at the same time, the death being in the same quarter would also point to that.
One or two points I think you have to remember - the IGI is not complete. When George and Marwin married they may have lived in a town whose church has not yet been transcribed by the LDS and then moved later. If you really wanted to know about Edward I would suggest that you check all churches in the area where they might possibly have lived. You will hopefully find this site useful for finding some of them,
http://www.genuki.org.uk/ and either write/visit the local Record Office to ask if they have the baptisms or even ask the LDS if they have them on film, just not transcribed on the site - remember that some churches just gave father's names so Marwin may not be mentioned. I must admit I'd be curious enough about Edward to investigate this further if it were me.
We don't know who wrote the names down when the babies were baptised - the minister probably wrote what they thought was the correct spelling, the parents possibly may not have even been able to write so it went unchecked.
In the early years after civil registration began, even after it became compulsory children often went unregistered, mainly from lack of funds. You can imagine if there was a choice between feeding the children or registering one of them, what do you think won?
As for the 1861 census for Elizabeth, if you are sure it's her husband that you have alone, then the scenario could be that she was visiting somebody and unexpectedly stayed overnight. If that family had already completed their form she probably wouldn't have been bothered, maybe thinking that her husband would have noted her as being at home. The husband however, thinking she would be enumerated where she was visiting didn't bother writing her name on the form and so she might have been missed. It's like the reverse of often finding children listed with both grandparents and parents on the same night, difficult to prove that they are the same person but imagine little ones clamouring to stay with grandma rather than going home and I would imagine that's how mistakes are made.
When it's a whole family missing that's a different matter and I usually believe that they are there somewhere, just a case of finding them however badly they have been either enumerated or transcribed.
You are lucky to have a few more names in the family to help pin them down - my own great grandma went unregistered in 1845 and no matter where I look I can find no baptism, the only possible marriage for her father seems rather unlikely and is nowhere to be found in the 1851 census. Later on she is working in various houses as a servant, so I have nothing to connect her to anybody, poor little orphan
